Pith Number

pith:7TE3SVEQ

pith:2014:7TE3SVEQBDQWJPZ2XGNBHTIOVJ

not attested not anchored not stored refs pending

New Quantitative Deformation Lemma and New Mountain Pass Theorem

Fode Zhang, Liang Ding, Shiqing Zhang

arxiv:1402.4602 v2 · 2014-02-19 · math.FA · math.AP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7TE3SVEQBDQWJPZ2XGNBHTIOVJ}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T02:44:47.415064Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fcc9b9549008e164bf3ab99a13cd0eaa613b2a3065366f05a2e4ea345e0ebe99

Aliases

arxiv: 1402.4602 · arxiv_version: 1402.4602v2 · doi: 10.48550/arxiv.1402.4602 · pith_short_12: 7TE3SVEQBDQW · pith_short_16: 7TE3SVEQBDQWJPZ2 · pith_short_8: 7TE3SVEQ

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/7TE3SVEQBDQWJPZ2XGNBHTIOVJ \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: fcc9b9549008e164bf3ab99a13cd0eaa613b2a3065366f05a2e4ea345e0ebe99

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1a5ff999146b0adb01ebeb244832f88847f57c1eeca1afdc128135f4fb21a00f",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://creativecommons.org/licenses/by/3.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2014-02-19T09:38:11Z",
    "title_canon_sha256": "ebbb3ad01a5679cdf267ab91be15676c9340bf1f997b33a841a06e82d97209c2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1402.4602",
    "kind": "arxiv",
    "version": 2
  }
}